Various high-speed semiconductor devices, which utilize a two-dimensional electron gas or a two-dimensional hole gas produced at a heterointerface as a channel layer, have been proposed. At a low temperature, the mobility of electrons in the two-dimensional electron gas is far higher than in a three-dimensional electron gas. When such a two-dimensional electron gas is spatially confined to decrease the degree of freedom of the movement of the electrons, a quasi one-dimensional electron gas is produced, and semiconductor devices utilizing the quasi one-dimensional electron gas as a channel layer have been developed. In the quasi one-dimensional electron gas, electrons move in one direction and scattering of the electrons (especially, phonon scattering) decreases as compared with the two-dimensional electron gas, so that the mobility further increases, resulting in a semiconductor device operating at higher speed.
FIG. 5 is a perspective view partly in a cross section of a prior art high-speed transistor utilizing the quasi one-dimensional electron gas. In FIG. 5, an intrinsic (hereinafter referred to as i type) AlGaAs layer 22 approximately 1000 angstroms thick, an i type GaAs layer 23 approximately 100 angstroms thick, and an n.sup.+ type AlGaAs layer 24 approximately 300 angstroms thick having an impurity concentration of 1.5.times.10.sup.18 cm.sup.-3 are successively disposed on a semi-insulating GaAs substrate 21. Source and drain electrodes 25 comprising, for example, AuGe/Ni/Au are spaced from each other by a prescribed interval on the n.sup.+ type AlGaAs layer 24. Alloy layers 29 beneath the source and drain electrodes 25 reach into the substrate 21 and the source and drain electrodes 25 make ohmic contacts with the semiconductor layers 22 to 24. An interlayer insulating film 26 comprising, for example, hydroxy silicon nitride (SiON) is disposed on the n.sup.+ type AlGaAs layer 24 where the source and drain electrodes are absent. An opening 27 penetrates a portion of the insulating layer 26 between the source and drain electrodes 25. A gate electrode 28 comprising aluminum or the like is connected to the substrate 21 and the semiconductor layers 22 to 24 which are exposed in the opening 27.
The i type AlGaAs layer 22, the i type GaAs layer 23, and the n.sup.+ type AlGaAs layer 24, which are exposed in the opening 27, i.e., which are connected to the gate electrode 28, are separated in a plurality of stripes running parallel to a direction connecting the source and drain electrodes 25.
FIGS. 6(a) and 6(b) are sectional views taken along a line VI--VI of FIG. 5. In these figures, the same reference numerals as in FIG. 5 designate the same or corresponding parts. The i type AlGaAs layer, the i type GaAs layer, and the n.sup.+ type AlGaAs layer are separated by notches 30, resulting in a plurality of fine stripes 40 each comprising i type AlGaAs layer 42, i type GaAs layer 43, and n.sup.+ type AlGaAs layer 44. The interval P between the adjacent stripes 40 is about 2000 angstroms. The gate electrode 28 fills up the notches 30 and contacts the side surfaces of each stripe 40.
A description is given of the operation. When no bias voltage is applied to the gate electrode 28, electrons are transferred from the n.sup.+ type AlGaAs layer 44 and stored in the i type GaAs layer 43, producing a two-dimensional electron gas 45 as shown in FIG. 6(a). When a negative bias voltage is applied to the gate electrode 28, a depletion layer in the i type GaAs layer 43 expands and the two-dimensional electron gas is concentrated in the center of the i type GaAs layer 43 as shown in FIG. 6(b). That is, the two-dimensional electron gas loses the degree of freedom in a direction perpendicular to an axis of the stripe, resulting in a quasi one-dimensional electron gas 50. In this state, a current flowing between the source and drain electrodes is carried by the one-dimensional electron gas. Concentration of the quasi one-dimensional electron gas 50 is controlled by the bias voltage applied to the gate electrode 28 to control the current flowing between the source and drain electrodes (I.sub.DS). Since the quasi one-dimensional electron gas serves as a carrier of the current, the mobility of electrons in the quasi electron gas is higher than that in the two-dimensional electron gas, whereby a high-speed FET due to a high mutual conductance (gm) is achieved. In addition, the quasi one-dimensional electron gas has less scattering of electrons than the two-dimensional electron gas, resulting in a low-noise FET.
In the prior art high-speed transistor constituted as described above, since the gate electrode 28 contacts the side surfaces of the stripes 40, gate capacitance increases, limiting the high speed property of the device. In addition, the gate electrode 28 is formed along the stripes 40 each about 2000 angstroms in height. However, precise patterning is difficult on such an uneven surface. Therefore, it is difficult to form a narrow gate electrode.